import os

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt
import plotly.express as px
import plotly.graph_objects as go

import plotly.io as pio
pio.renderers.default = "plotly_mimetype+notebook+vscode"

# function used in case we would like to select desired timestamp
def trunc_df(df):
    start = pd.to_datetime('2020-07-01 19:30:00')
    end = pd.to_datetime('2020-08-01 19:30:00')
    ret_df = df.loc[start:end]
    return ret_df

# to always have the newest plot versions, delete file before creating new one
def remove_file_if_exists(file_path):
    if os.path.exists(file_path):
        os.remove(file_path)

# svd global variables
SVD_FOLDER_PATH = 'svd_plots'
SVD_RECONSTUCTION_FOLDER_PATH = f'{SVD_FOLDER_PATH}/reconstuction'
SVD_COLUMN = 'tempC'

# recreate directories
if not os.path.exists(SVD_FOLDER_PATH):
    print(f'Creating folder {SVD_FOLDER_PATH}')
    os.mkdir(SVD_FOLDER_PATH)
if not os.path.exists(SVD_RECONSTUCTION_FOLDER_PATH):
    print(f'Creating folder {SVD_RECONSTUCTION_FOLDER_PATH}')
    os.mkdir(SVD_RECONSTUCTION_FOLDER_PATH)

Prepare Data for SVD Analysis

# function to create csv file used for analysis
def create_svd_df(column_value):
    FULL_DATA_FILENAME = 'data.csv.gz'
    OUTPUT_FILENAME = f'data_svd_{column_value}.csv'
    
    columns_to_read = ['date_time', 'city', column_value] 
    df = pd.read_csv(FULL_DATA_FILENAME, usecols=columns_to_read, compression='gzip')
    unique_towns = sorted(list(df['city'].unique()))
    
    new_index = pd.date_range(
        start=df.iloc[0]['date_time'], 
        end=df.iloc[-1]['date_time'],
        freq='3h'
    )
    data = np.array(df[column_value])
    data = data.reshape(len(new_index), len(unique_towns))

    ret_df = pd.DataFrame(
        data=data, 
        columns=unique_towns, 
        index=new_index, 
        dtype=float
    )
    ret_df.to_csv(OUTPUT_FILENAME)

GEOLOCATION_FILENAME = 'geo_position.csv'
df_geolocation = pd.read_csv(GEOLOCATION_FILENAME).sort_values(by='CITY')
unique_towns = sorted(list(df_geolocation['CITY'].unique()))  # get unique names of towns ordered by name

print(f'Doing analisys for {SVD_COLUMN}')   
SVD_DATA_FILENAME = f'data_svd_{SVD_COLUMN}.csv'

if not os.path.exists(SVD_DATA_FILENAME):
    print(f'Creating svd file for {SVD_COLUMN}')
    create_svd_df(column_value=SVD_COLUMN)
    print('File created!')

Doing analisys for tempC

SVD

print(f'Loading svd file for {SVD_COLUMN}')
SVD_DATA_FILENAME = f'data_svd_{SVD_COLUMN}.csv'
df_svd = pd.read_csv(SVD_DATA_FILENAME, index_col=0)
df_svd.index = pd.to_datetime(df_svd.index)

# df_svd = trunc_df(df_svd)
svd_A = np.array(df_svd)

# build matrix U, S, V
svd_U, svd_S, svd_V = np.linalg.svd(svd_A, full_matrices=False)

Loading svd file for tempC

Precision of SVD Resconstrucion

# function to calculate and plot precision of svd reconstruction
def svd_precision(svd_S):
    SVD_PRECISION_FILENAME = f'{SVD_FOLDER_PATH}/{SVD_COLUMN}_svd_precision.png'
    remove_file_if_exists(SVD_PRECISION_FILENAME)
    
    fig = go.Figure(
        data=[go.Bar(
                x=np.arange(np.size(svd_S)),
                y=np.cumsum(svd_S / np.sum(svd_S))
            )
        ]
    )
    
    fig.update_layout(
        title_text='SVD Precision', 
        title_x=0.5,
        xaxis_title='Rank', 
        yaxis_title='Precision'
    )
    fig.update_yaxes(range=[0.5, 1])
    fig.write_image(SVD_PRECISION_FILENAME)
    fig.show()

# Calculating svd reconstruction precision
svd_precision(svd_S)

Full Reconstruction & Lower Rank Reconstruction

# full reconstruction - matrix svd_Ar
svd_Ar = np.dot(svd_U * svd_S, svd_V)
print(f'Diff: {np.mean(np.abs(svd_A - svd_Ar))}')

# lower rank reconstruction - matrix svd_Ar
k = 5
svd_Ar = np.dot(svd_U[:,:k] * svd_S[:k], svd_V[:k, :])

print(f'Diff reconstruction: {np.mean(np.abs(svd_A - svd_Ar))}')

Diff: 1.88244953759014e-14
Diff reconstruction: 0.256627458260023

Average SVD Error

# function to calculate and plot average error of svd for k=n
def svd_average_error(svd_A, svd_Ar, k, unique_towns):
    SVD_AVG_ERR_FILENAME = f'{SVD_FOLDER_PATH}/{SVD_COLUMN}_svd_avg_err.png'
    remove_file_if_exists(SVD_AVG_ERR_FILENAME)

    svd_err = np.average(np.abs(svd_A - svd_Ar), axis=0)
    asix_range = np.arange(0, len(unique_towns))

    fig = go.Figure(data=[go.Bar(x=asix_range,
                                 y=svd_err
                                 )])

    fig.update_layout(
        title_text='SVD Average Error', title_x=0.5,
        yaxis_title=f'Average error of reconstruction with rank k={k}',
        xaxis=dict(tickmode='array',
            tickvals=asix_range,
            ticktext=unique_towns
        )
    )
    fig.update_xaxes(tickangle=90)
    fig.write_image(SVD_AVG_ERR_FILENAME)
    fig.show()

# Calculating average error
svd_average_error(
    svd_A=svd_A, 
    svd_Ar=svd_Ar, 
    k=k, 
    unique_towns=unique_towns
)

Dates to Concept - SVD_U

# function to plot dates to concept for k=n
def svd_dates_to_concept(k, index, svd_U):
    SVD_DTC_FILENAME = f'{SVD_FOLDER_PATH}/{SVD_COLUMN}_svd_dates_to_concept.png'
    remove_file_if_exists(SVD_DTC_FILENAME)
    all_plots = []
    for i in range(k):
        all_plots.append(go.Scatter(x=index, y=svd_U[:, i], name=f'k={i}'))
    
    fig = go.Figure(data=all_plots)
    fig.write_image(SVD_DTC_FILENAME)
    fig.update_layout(xaxis=dict(rangeslider=dict(visible=True)))
    fig.show()

# dates to concept
svd_dates_to_concept(
    k=k, 
    index=df_svd.index, 
    svd_U=svd_U
)

Towns to Concept - SVD_V

# function to plot towns to concept for k=n
def svd_towns_to_concept(k, svd_V, unique_towns):
    SVD_TTC_FILENAME = f'{SVD_FOLDER_PATH}/{SVD_COLUMN}_svd_towns_to_concept.png'
    remove_file_if_exists(SVD_TTC_FILENAME)
    
    asix_range = np.arange(0, len(unique_towns))
    all_plots = []
    for i in range(k):
        all_plots.append(go.Bar(x=asix_range, y=svd_V[i, :], name=f'{i}'))
        
    fig = go.Figure(data=all_plots)
    
    fig.update_layout(
        title_text=f'Towns to Concept for k={k}', 
        title_x=0.5,
        xaxis=dict(
                tickmode='array',
                tickvals=asix_range,
                ticktext=unique_towns
        )
    )
    
    fig.update_xaxes(tickangle=90)
    fig.write_image(SVD_TTC_FILENAME)
    fig.show()

# towns to concept
svd_towns_to_concept(
    k=k,
    svd_V=svd_V, 
    unique_towns=unique_towns
)

SVD Maps

# plot map with values from SVD_V (towns to concept)
def plot_svd_map(vector, k, data_geo):
    SVD_MAP_FILENAME = f'{SVD_FOLDER_PATH}/{SVD_COLUMN}_svd_map_k{k}.png'
    remove_file_if_exists(SVD_MAP_FILENAME)
    
    data_geo['VALUES'] = vector
    px.set_mapbox_access_token(open(".mapbox_token").read())
    
    fig = px.scatter_mapbox(
        data_geo,
        size = [2] * len(data_geo.index), 
        lat="LAT", 
        lon="LNG", 
        color="VALUES",
        hover_name="CITY",
        color_continuous_scale=px.colors.cyclical.Phase,
    )
    
    fig.update_layout(
        height = 700,
        margin = {
            'l':5,
            'r':5,
            't':5,
            'b':5,
        },
        autosize=True,
        mapbox = {
            'style': "open-street-map",
            'zoom': 7.5
        }
    )
    fig.write_image(SVD_MAP_FILENAME)
    fig.show()

# plot maps
for i in range(k):
    print(f'Ploting map for k = {i}')
    plot_svd_map(
        vector=svd_V[i, :], 
        k=i, 
        data_geo=df_geolocation.copy()
    )

Ploting map for k = 0

Ploting map for k = 1

Ploting map for k = 2

Ploting map for k = 3

Ploting map for k = 4

SVD Reconstruction

# reconstruct temperatures of unique towns using svd
def svd_reconstruct(unique_towns, df_svd, svd_A, svd_U, svd_S, svd_V, k):
    print(f'Saving reconstructins to {SVD_RECONSTUCTION_FOLDER_PATH}')
    for iloc, location in enumerate(unique_towns):
        SVD_RESONSTRUCTION_FILENAME = f'{SVD_RECONSTUCTION_FOLDER_PATH}/{SVD_COLUMN}_svd_reconstruction_plot_{location}.png'
        remove_file_if_exists(SVD_RESONSTRUCTION_FILENAME)
        
        fig = plt.figure(figsize=(20, 10), tight_layout=True)
        legend_handles = []
        legend_labels = []

        plt_orig, = plt.plot(df_svd[location], marker='o', ls='', c='r', ms=1)
        legend_handles.append(plt_orig)
        legend_labels.append('Original data')

        a_cum = np.zeros(svd_A.shape[0])
        for i in range(k):
            a_k = np.dot(svd_U[:, i] * svd_S[i], svd_V[i, iloc])
            flbtw_k = plt.fill_between(df_svd.index, a_cum, a_cum + a_k, alpha=0.3, label=f'k= {i}')
            legend_handles.append(flbtw_k)
            legend_labels.append(f'k= {i}')
            a_cum += a_k

        plt_recon, = plt.plot(df_svd.index, a_cum, marker='s', ls='--', c='b', lw=1, ms=1)
        legend_handles.append(plt_recon)
        legend_labels.append('Reconstruction')

        plt.legend(legend_handles, legend_labels)
        plt.ylim(df_svd[location].min() - 2, df_svd[location].max() + 2)
        fig.savefig(SVD_RESONSTRUCTION_FILENAME, dpi=90)
        
        if location == 'Rijeka':
            plt.title(f'Reconstruction for {location}')
            plt.show()
            
        plt.close(fig)

# SVD reconstruction temperature
svd_reconstruct(
    unique_towns=unique_towns, 
    df_svd=df_svd, 
    svd_A=svd_A, 
    svd_U=svd_U, 
    svd_S=svd_S, 
    svd_V=svd_V, 
    k=k
)

Saving reconstructins to svd_plots/reconstuction

Export to HTML

# save notebook before nbconvert
import IPython

%%javascript
IPython.notebook.save_notebook()

# export notebook results to HTML
!jupyter nbconvert --to=HTML svd.ipynb

[NbConvertApp] WARNING | pattern 'svd.ipynb\\' matched no files
This application is used to convert notebook files (*.ipynb)
        to various other formats.

        WARNING: THE COMMANDLINE INTERFACE MAY CHANGE IN FUTURE RELEASES.

Options
=======
The options below are convenience aliases to configurable class-options,
as listed in the "Equivalent to" description-line of the aliases.
To see all configurable class-options for some <cmd>, use:
    <cmd> --help-all

--debug
    set log level to logging.DEBUG (maximize logging output)
    Equivalent to: [--Application.log_level=10]
--show-config
    Show the application's configuration (human-readable format)
    Equivalent to: [--Application.show_config=True]
--show-config-json
    Show the application's configuration (json format)
    Equivalent to: [--Application.show_config_json=True]
--generate-config
    generate default config file
    Equivalent to: [--JupyterApp.generate_config=True]
-y
    Answer yes to any questions instead of prompting.
    Equivalent to: [--JupyterApp.answer_yes=True]
--execute
    Execute the notebook prior to export.
    Equivalent to: [--ExecutePreprocessor.enabled=True]
--allow-errors
    Continue notebook execution even if one of the cells throws an error and include the error message in the cell output (the default behaviour is to abort conversion). This flag is only relevant if '--execute' was specified, too.
    Equivalent to: [--ExecutePreprocessor.allow_errors=True]
--stdin
    read a single notebook file from stdin. Write the resulting notebook with default basename 'notebook.*'
    Equivalent to: [--NbConvertApp.from_stdin=True]
--stdout
    Write notebook output to stdout instead of files.
    Equivalent to: [--NbConvertApp.writer_class=StdoutWriter]
--inplace
    Run nbconvert in place, overwriting the existing notebook (only
            relevant when converting to notebook format)
    Equivalent to: [--NbConvertApp.use_output_suffix=False --NbConvertApp.export_format=notebook --FilesWriter.build_directory=]
--clear-output
    Clear output of current file and save in place,
            overwriting the existing notebook.
    Equivalent to: [--NbConvertApp.use_output_suffix=False --NbConvertApp.export_format=notebook --FilesWriter.build_directory= --ClearOutputPreprocessor.enabled=True]
--no-prompt
    Exclude input and output prompts from converted document.
    Equivalent to: [--TemplateExporter.exclude_input_prompt=True --TemplateExporter.exclude_output_prompt=True]
--no-input
    Exclude input cells and output prompts from converted document.
            This mode is ideal for generating code-free reports.
    Equivalent to: [--TemplateExporter.exclude_output_prompt=True --TemplateExporter.exclude_input=True --TemplateExporter.exclude_input_prompt=True]
--allow-chromium-download
    Whether to allow downloading chromium if no suitable version is found on the system.
    Equivalent to: [--WebPDFExporter.allow_chromium_download=True]
--disable-chromium-sandbox
    Disable chromium security sandbox when converting to PDF..
    Equivalent to: [--WebPDFExporter.disable_sandbox=True]
--show-input
    Shows code input. This flag is only useful for dejavu users.
    Equivalent to: [--TemplateExporter.exclude_input=False]
--embed-images
    Embed the images as base64 dataurls in the output. This flag is only useful for the HTML/WebPDF/Slides exports.
    Equivalent to: [--HTMLExporter.embed_images=True]
--log-level=<Enum>
    Set the log level by value or name.
    Choices: any of [0, 10, 20, 30, 40, 50, 'DEBUG', 'INFO', 'WARN', 'ERROR', 'CRITICAL']
    Default: 30
    Equivalent to: [--Application.log_level]
--config=<Unicode>
    Full path of a config file.
    Default: ''
    Equivalent to: [--JupyterApp.config_file]
--to=<Unicode>
    The export format to be used, either one of the built-in formats
            ['asciidoc', 'custom', 'html', 'latex', 'markdown', 'notebook', 'pdf', 'python', 'rst', 'script', 'slides', 'webpdf']
            or a dotted object name that represents the import path for an
            ``Exporter`` class
    Default: ''
    Equivalent to: [--NbConvertApp.export_format]
--template=<Unicode>
    Name of the template to use
    Default: ''
    Equivalent to: [--TemplateExporter.template_name]
--template-file=<Unicode>
    Name of the template file to use
    Default: None
    Equivalent to: [--TemplateExporter.template_file]
--theme=<Unicode>
    Template specific theme(e.g. the name of a JupyterLab CSS theme distributed
    as prebuilt extension for the lab template)
    Default: 'light'
    Equivalent to: [--HTMLExporter.theme]
--writer=<DottedObjectName>
    Writer class used to write the
                                        results of the conversion
    Default: 'FilesWriter'
    Equivalent to: [--NbConvertApp.writer_class]
--post=<DottedOrNone>
    PostProcessor class used to write the
                                        results of the conversion
    Default: ''
    Equivalent to: [--NbConvertApp.postprocessor_class]
--output=<Unicode>
    overwrite base name use for output files.
                can only be used when converting one notebook at a time.
    Default: ''
    Equivalent to: [--NbConvertApp.output_base]
--output-dir=<Unicode>
    Directory to write output(s) to. Defaults
                                  to output to the directory of each notebook. To recover
                                  previous default behaviour (outputting to the current
                                  working directory) use . as the flag value.
    Default: ''
    Equivalent to: [--FilesWriter.build_directory]
--reveal-prefix=<Unicode>
    The URL prefix for reveal.js (version 3.x).
            This defaults to the reveal CDN, but can be any url pointing to a copy
            of reveal.js.
            For speaker notes to work, this must be a relative path to a local
            copy of reveal.js: e.g., "reveal.js".
            If a relative path is given, it must be a subdirectory of the
            current directory (from which the server is run).
            See the usage documentation
            (https://nbconvert.readthedocs.io/en/latest/usage.html#reveal-js-html-slideshow)
            for more details.
    Default: ''
    Equivalent to: [--SlidesExporter.reveal_url_prefix]
--nbformat=<Enum>
    The nbformat version to write.
            Use this to downgrade notebooks.
    Choices: any of [1, 2, 3, 4]
    Default: 4
    Equivalent to: [--NotebookExporter.nbformat_version]

Examples
--------

    The simplest way to use nbconvert is

            > jupyter nbconvert mynotebook.ipynb --to html

            Options include ['asciidoc', 'custom', 'html', 'latex', 'markdown', 'notebook', 'pdf', 'python', 'rst', 'script', 'slides', 'webpdf'].

            > jupyter nbconvert --to latex mynotebook.ipynb

            Both HTML and LaTeX support multiple output templates. LaTeX includes
            'base', 'article' and 'report'.  HTML includes 'basic', 'lab' and
            'classic'. You can specify the flavor of the format used.

            > jupyter nbconvert --to html --template lab mynotebook.ipynb

            You can also pipe the output to stdout, rather than a file

            > jupyter nbconvert mynotebook.ipynb --stdout

            PDF is generated via latex

            > jupyter nbconvert mynotebook.ipynb --to pdf

            You can get (and serve) a Reveal.js-powered slideshow

            > jupyter nbconvert myslides.ipynb --to slides --post serve

            Multiple notebooks can be given at the command line in a couple of
            different ways:

            > jupyter nbconvert notebook*.ipynb
            > jupyter nbconvert notebook1.ipynb notebook2.ipynb

            or you can specify the notebooks list in a config file, containing::

                c.NbConvertApp.notebooks = ["my_notebook.ipynb"]

            > jupyter nbconvert --config mycfg.py

To see all available configurables, use `--help-all`.